Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e6;
int n, pos[maxn + 10], t[maxn + 10], f[maxn + 10];
int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		int x; scanf("%d", &x); pos[x] = i;
	}
	for (int i = n - 1; i >= 1; --i) {
		if (!t[i + 1]) {
			if (pos[i] < pos[i + 1]) t[i] = 0;
			else {
				t[i] = 1; f[i] = i + 1;
			}
		} else {
			int x = pos[f[i + 1]], y = pos[i], z = pos[i + 1];
			if ((x < y) + (y < z) + (z < x) == 2) {
				t[i] = t[i + 1]; f[i] = f[i + 1];
			} else {
				t[i] = t[i + 1] + 1; f[i] = i + 1;
			}
		}
	}
	printf("%d", t[1]);
}